The "me" in "no te me hagas el bobo" is a solidarity pronoun. It's used to create a stronger link between the speaker and the audience. This is a topic that has been studied in sociolinguistics (google "solidarity pronoun"), and some languages such as Galician and Basque (as far as I know) have special constructs to express it.
Basically, "no te hagas el ...

Yes, It has an additional meaning. De, a, hacia, desde, etc are prepositions, and they are used to fine tune the verb they are with.
De usually points to the passive recipient of the action (I don't know the actual term). For example:
Escaparse de la policia - To escape from the cops
In this case you're doing the escaping, but the cops are being the ...

W...wait.
Olvidar works like forget in English. The one doing the forgetting is the subject and the forgotten thing is the object.
Yo olvidé mi cita. Yo olvidé mis llaves
So the verb must match in form the one doing the forgetting.
However, you are also seeing examples of passive construction with "se".
Se me olvidó la cita. Se me olvidaron las ...

This is a kind of passive called "Pasiva refleja". "Pasiva refleja" is the passive voice most used in Spanish. RAE explains it here. The way of forming it
Se + < transitive verb > + < nominal element >
The verb will be always conjugated in 3rd person. If the nominal element is singular it will be 3rd person singular, but if that nominal element ...

You seem cute. (Depends on context. It could also be used to imply someone thinks they're cute.)
The object pronoun is reflexive and is used to establish the passive voice. verse and parecer can be used interchangeably most of the time in this context (to seem).
You look bad.
Here, se is used to establish the passive voice, and the te in te ve is a direct ...

It is necessary to show the correct use of 'celebra' in a passive voice:
With se: (se celebra = es celebrado/celebrada) -> (it) is celebrated
Se celebra principalmente en Mexico y Estados Unidos.
It is celebrated mainly in Mexico and USA.
Without 'se', 'celebra' turns into active voice = (he/she/it celebrates)
A deeper explanation can be ...

The word "se" is used whenever you want to point that something is part of, property of, like when you use "for himself/herself" or "his/her".
So putting this as examples:
Mi hermano menor se rompió la mayoría de vasos.
means "my little brother broke the mayority of his glasses" (but since the bother doesn't have glasses inside his body nor the glasses ...

Yes, and it's the rule you wrote yourself, adding se to the infinitive.
As all infinitives end in -ar, -er or -ir, adding se is totally regular and consistent.
At least grammatically, because there may be some verbs that are semantically unable to become reflexive, I.E. it wouldn't make any sense that the subject and the object be the same, although I'm ...

I'm not sure what you're looking for. Maybe the problem is that you need an appropriate question so then you could easily find the answer in a book or on Internet. (I remember the great book "The hitchhiker's guide to the galaxy"...)
But maybe I can help you anyway. I'll write in spanish because I express myself better in that way.
Voy a intentar ...

Although the example in the question are impersonal se and not reflexive se, they do follow many of the same rules. The meanings are completely different, but look at these examples:
Spanish is spoken. Se habla español.
Spanish speaks itself. Se habla español. (Español se habla.)
The word order could go either way.
Cars are sold. Se ...

se is not reflexive in neither example you gave, it's only reflexive when it can be translated to him-/her-/itself
For example: se miró al espejo : he looked himself on the mirror
edit: This isn't a golden rule, there are exceptions, like se ató los zapatos (he tied his shoelaces) which doesn't involve himself, but because although semantically the shoes ...

serme = ser + me and means "to be" in its infinitive reflexive form. "Mentirme" is of the same form, mentir + me.
This year I decided to be faithful to myself and not lie to myself.
You can add the reflexive pronouns to the end of infinitives, gerunds and affirmative imperative verbs.

You find yourself pretty.
This is for ego talking. If I say "Me veo bien", that means I'm happy with my body, with my level of English...
You look bad.
This is an opinion on how are you, but is used for a general statement, something that everyone can notice.
I can see you're ok!
This is the same as 2, but with the subject giving an opinion. An example:
...

Some grammarians call pronominal verbs (verbos pronominales) those verbs that use a reflexive pronoun but do not have a reflexive meaning.
The reflexive pronoun can appear in five basic cases:
True reflexive verbs or reflexive actions:
Pedro se llamó a la casa desde el celular. — Pedro rang himself home from his mobile.
Reciprocal actions:
...

The web you link has a mistake. As you correctly noticed, the examples for the reflexive use are wrong. It looks like somebody just cut and pasted the examples for the transitive use instead of inserting the right ones. Your made-up example is a good one indeed.
Casar is a funny verb because, strictly speaking, it should always be reciprocal. Two people ...

Se celebra translates to They celebrate
which is how we, English speakers, would say it.
For instance, Aquí se celebra Navidad en Pascua
Here, they celebrate Christmas on Easter
Not they as in 3rd person plural, but rather, they as in the people here.
When we are giving instructions we tend to say things like
You mix the milk in with the eggs
Se ...